A pair of trolls urinate into a castellated fountain in one drawing ……

Project for a metropolitan cathedral in the form of a Greek cross with a domed centre by Etienne-Louis Boulée, 1782, from Disappear Here: On Perspective and Other Kinds of Space.Photograph: RIBA Collections

A pair of trolls urinate into a castellated fountain in one drawing, beneath an image of two momentous wedge-shaped structures, stretching into the infinite distance on a gridded landscape. An energetic sketch by Edwin Lutyens hangs nearby, depicting a monumental war memorial from a worm’s-eye-view, while in another image a group of Renaissance gentlemen busy themselves marking out the plan of a temple in a picturesque landscape.

These four disparate drawings, made over the last five centuries, have one thing in common: the powerful use of perspective. They appear in a new exhibition at the Royal Institute of British Architects, conceived by architect Sam Jacob and curator Marie Bak Mortensen, which aims “to reveal and undo the tyranny of perspective” in Jacob’s words, and to show “how the representation of architecture shapes architecture itself”.

Design for a ceiling with columns and coffered arches, Italy, c1700, unknown designer, from Disappear Here: On Perspective and Other Kinds of Space. Photograph: RIBA Collections

The origins of the show lie in a high-minded plan for a series of exhibitions based on the seven-volume treatise of the Italian Renaissance theorist Sebastiano Serlio, Seven Books of Architecture, which covers everything from housing to the five classical orders (followed by an unmissable bonus volume, The Extraordinary Book of Doors). The book on perspective has been taken as a loose starting point, a theme to allow the curators to rummage through the RIBA collection and pick out 15 or so drawings that they liked the look of, with a few more supplied by collector Niall Hobhouse. Their intriguing haul has been thrown on the wall in a seemingly random order, without chronology or overarching idea, save for trying to connect up some of the vanishing points.

A 1970s collage by radical Italian group Superstudio hangs near a fragment of a cornice by the student Palladio in the 1530s, scrawled naively on the back of another drawing. It is not very accomplished, and it’s hung too high up to see it properly (maybe for the best) – perhaps explaining why Palladio would never use perspective drawings in his own work again. There is more charming naivety in a 1600s drawing by John Smythson of his design for a Jacobean house with a castellated wing, where he has clearly been befuddled by his attempt to use multiple vanishing points, leaving wonky facades zig-zagging across the page. His style shares similarities with a drawing made more than 300 years later by French designer Jean-Charles Moreux, although by the 1920s Moreux has stripped his vanishing points down to one, giving his sparse interior a simple, diagrammatic air.

Meanwhile, marrying the sublime with the suburban, the vertiginous interior of Etienne-Louis Boulée’s 1782 proposal for a gargantuan metropolitan cathedral in Paris is contrasted with the prosaic interior of a 1970s conservatory. Ernő Goldfinger’s working perspective for a tower in the City of London is compared with an 18th-century aerial view of a sprawling country estate, of the kind commissioned by proud clients to impress upon visitors the extent of their empires.

Design for a House With a Castellated Wing by John Smythson, 1600. Photograph: RIBA Collections

Adding an extra layer of disorientation to the jumbled hang, the small gallery’s walls have been transformed into a trompe-l’oeil stage set, with a skewwhiff mural of columns and doorways. The unstable feeling is exaggerated by a continuous mirrored skirting around the base of the walls and a fragment of an octagonal pergola completed by a mirrored corner. A forced perspectival entrance makes for a fun opening, and will keep small children entertained.

Bringing the use of perspective up to date, Jacob has also worked with a video game designer to produce a three-sided projection in a side gallery, where you are immersed in a meteor shower of flying gazebos and triumphal arches, fragments from architectural history hurtling past from a single central vanishing point. Rendered in shades of pink and teal, it would make for a nice enough screensaver, but it’s not clear what it’s trying to say. It is a leap from the 1970s collages of Superstudio to the present-day possibilities of the Unity gaming engine, and it’s odd not to include any other computer-aided perspective from the past half-century of architectural drawing in the selection, given that AutoCad and its ilk have created a world of photorealistic perspectives on demand.

In Jacob’s catalogue essay, he expands on the fascinating history of perspective, citing the transition from Alberti to Brunelleschi, and Erwin Panofsky’s 1920s writings, which posited that linear perspective could only occur when a particular conception of the universe emerged, “when a new religious conception of a singular, divine omnipresence meant that the infinite, and so the vanishing point, could be imagined”. It is no coincidence, he suggests, that perspective developed within the mercantile contexts of Renaissance Florence and Venice, where the measurement of goods was fundamental to the accumulation of wealth and power. These ideas are perhaps latent in some of the drawings on show, but it wouldn’t have hurt to do a little more to bring them to life – to put the theme of perspective more in perspective.

Disappear Here is at the Royal Institute of British Architects, London from 2 May to 7 October.